1. Field of the Invention
The present invention relates to a method for producing optical multilayered optical filters, for appropriately splitting/merging signal lights having plural wavelength convoluted, used in an optical communication system sending/receiving wavelengths multiplexed light communications, and to a method for ICE operating the genetic algorithm for extracting the most suitable combination from candidates of complex combination.
2. Description of the Prior Art
As wavelength-multiplexed light communications have been developed, there are needs for multilayered splitting/merging filters having such characteristics as a narrow passband or small para-reflex characteristics.
For methods of designing multilayered optical filters each layer of which has refractive index Ni and thickness Di based on a desired optic characteristics, in general, it has been common to use a method of thickness optimization such as described in Japanese Published Unexamined Patent Application No. 2650048, by determining in advance refractive index Ni of each layer composing the filter, to preset the thickness Di, to determine optical characteristics for each wavelength, to change the thickness Di, to optimize the thickness Di so as to have maximum in the optical characteristics.
As another method of optimization, there is only a trial and error method in which refractive index of a layer is altered, and the thickness for every layer is optimized again.
In accordance with the method as described above, since the refractive index Ni is predetermined, the degree of freedom of design is not insufficient, and furthermore the results may often fall into a local solution.
In addition, there are a huge number of combinations of Ni and Di in a multilayered optical filter so that the optimization requires very long time for selection; therefore the selection of the most optimized combination has been practically impossible.
In the Prior Art local resolution obtained by using the thickness optimization method as have been described above was needed and the only practical result.
The present invention been made in view of the above circumstances and has an object to overcome the above problems and to provide a method of production of multilayered optical filters, used in the designing of multilayered optical filters having such complex combinations as described above, for selecting the most optimized combination of refractive index Ni and thickness Di for each of layers without falling into a local solution.
Also, the inventors of the present invention have been realized a method for selecting the most optimized solution, in order to determine the most optimized or almost optimized solution, in which a genetic algorithm (abbreviated as GA hereinafter) are used for converting the problems of optimization into the genetic sequences, such as the problems of optimization of the combinations of refractive index Ni and thickness Di in each layer in the designing of multilayered optical filters, comprising the steps of:
generating pattern groups, for generating pattern groups each comprised of a plurality of patterns;
extracting at least two patterns from within the generated group of patterns;
mutating and crossing over for generating new patterns by mutating or crossing over the extracted patterns;
evaluating for calculating the fitness of the optimization problem of the groups comprising the extracted patterns and newly generated patterns, for each of mutation and cross-over steps;
selecting to decrease the number of groups including extracted patterns and newly generated patterns to the number of extracted patterns;
substituting the selected patterns in place of the patterns extracted from the pattern groups, and
altering the contents of pattern groups by repeating between the extracting step and the selecting step.
The step of selecting in the genetic algorithm comprises either elite method, for selecting patterns of the predetermined numbers in the order of fitness among the object pattern group and removing others, or elite-roulette method, for selecting some patterns by using the elite method, and others by using the roulette method and removing the rest.
In both selection methods, there is no restriction of pattern selection, so that any duplicated patterns having the identical pattern elements were not rejected. If the selected patterns are filled with patterns having the identical elements, in some optimization problems, patterns having the same elements are inserted into the pattern group, and after repeating the genetic algorithm steps as described above, pattern group are totally filled with the patterns having the identical elements. This may result in an unexpected error in the retrieval search of the most optimized solution.
Often the search results obtained by the GA as above may be a local solution, which may or may not satisfy the goal.
Another object of the present invention is to avoid, in GA the predominance of selected pattern and of pattern group with the patterns having the same elements by preventing the patterns having the identical elements from coexisting in the selection patterns in order to retrieval search not only a local solution but also the most suitable one.
A method for producing multilayered optical filters comprises:
a generating step for generating a initial pattern comprising a matrix given by
P=(X1, X2, X3 . . . , XS)xe2x80x83xe2x80x83(1)
which is comprised of elemental matrices Xi, each of which comprises as element refractive index and thickness of i layers (i is an integer equal to or more than 1) of a multilayered optical filter having S layers (S is an integer equal to or more than 1);
a reproducting/mutating step for either increasing or decreasing, in an arbitrary element Xi of the initial pattern, either the refractive index or thickness of the initial pattern by a predetermined number, in terms of the initial pattern, to generate a predetermined number of mutation patterns which are mutually different one from other;
a cross over step for selecting at least one pair of patterns from the mutated patterns generated in the reproducting/mutating step and the initial patterns to cross over, in the pair of patterns selected, the matrix Xi in the pattern and/or the matrix obtained by the mutation of the matrix by the predetermined number to generate a predetermined number of crossed over patterns;
a selecting step for selecting the desired number of patterns having the most appropriate optical characteristics from the mutated pattern group generated in the reproducting/mutating step, the crossed over pattern group, and the pattern group comprised of the initial patterns; and
a repeating step for repeating a series of algorithmic process steps comprised of the reproducting/mutating step, the cross over step, and the selecting step,in terms of the predetermined number of patterns selected in the selecting step instead of the initial patterns, until the optical characteristics of the selected patterns obtained in the immediately preceding algorithmic steps may conform to the desired error range for the desired optical characteristics.
In accordance with the method of producing multilayered optical filters in accordance with the present invention, the repetition of a series of algorithmic process steps allows each layer in a multilayered optical filter to be set in such a manner as the optic characteristics may conform to a specific desired range. This may result in a better design and production of multilayered optical filters when compared with the conventional designing method.
When a series of the algorithmic process steps comprised of the reproducting and mutating step, the cross over step, and the selecting step, if the optical characteristics of the selected pattern obtained from the algorithmic process steps match with the optical characteristics of the selected pattern obtained from one of the repetitions preceding to the former, a second initial pattern, which is different from the initial pattern, is preferably set to repeat the algorithmic process steps using this second initial pattern.
In accordance with the method disclosed herein, even when the optical characteristics of the design obtained by the repetition of a series of algorithmic process steps show no progress in improvement, then the algorithm may recover from this stacked condition by restarting from the second initial pattern.
Preferably, the second initial pattern may be chosen which is generated by either increasing or decreasing the refractive index or the thickness in the selection patterns having the most appropriate optical characteristics obtained in the preceding process steps.
In accordance with the method disclosed herein, the information about optical elements, effective to the improvement of optical characteristics, in the patterns generated until the optical characteristics have been matched with, may be effectively used for the second initial pattern, allowing better and faster design of multilayered optical filters with better optical characteristics.
Another method for producing multilayered optical filters comprises:
a generating step for generating a initial pattern comprising a matrix given by
P=(X1, X2, X3 . . . , XS)xe2x80x83xe2x80x83(1)
which is comprised of elemental matrices Xi, each of which comprises as element refractive index and thickness of i layers (i is an integer equal to or more than 1) of a multilayered optical filter having S layers (S is an integer equal to or more than 1);
a first reproducting/mutating step for duplicating a predetermined number of patterns from the initial pattern for either increasing or decreasing, in an arbitrary element Xi of the duplicated pattern, either the refractive index or thickness of the initial pattern by a predetermined number;
a first selecting step for selecting the desired number of patterns having the most appropriate optical characteristics from the groups consisted of the mutation patterns generated in the immediately preceding step and the initial pattern;
a cross over step for selecting at least one set of a pair of patterns from the selected patterns generated in the selection step to cross over, the matrix Xi in the pattern and/or the matrix obtained by the mutation of the matrix by the predetermined number to generate a predetermined number of crossed over patterns;
a second reproducting/mutating step for selecting and replicating at least one arbitrary pattern from the pattern groups consisted of the crossed over pattern group and the selected pattern group, to generate mutated pattern by either increasing or decreasing, in an arbitrary element Xi of the duplicated pattern and/or in an element of the matrix obtained by the mutation of the matrix by the predetermined number;
a second selection step for selecting the desired number of patterns having the most appropriate optical characteristics from the pattern groups consisted of the mutated pattern group, the crossed over pattern group, and the selected pattern group;
a repeating step for repeating a series of algorithmic process steps comprised of the first reproducting/mutating step, the first selecting step, the cross over step, the second reproducting/mutating step, and the second selecting step, in terms of the predetermined number of patterns selected in the second selecting step instead of the initial pattern, until the optical characteristics of the second selected patterns obtained in the immediately preceding algorithmic steps may conform to the desired error range for the desired optical characteristics.
In accordance with another method of producing multilayered optical filters in accordance with the present invention, the repetition of a series of algorithmic process steps allows each layer in a multilayered optical filter to be set in such a manner as the optic characteristics may conform to a specific desired range. This may result in a better design and production of multilayered optical filters when compared with the conventional designing method.
When a series of the algorithmic process steps comprised of the first reproducting/mutating step, the first selecting step, the cross over step, the second reproducting/mutating step, and the second selecting step, if the optical characteristics of the second selected pattern obtained from the algorithmic process steps match with the optical characteristics of the second selected pattern obtained from one of the repetitions preceding to the former, a second initial pattern, which is different from the initial pattern, is preferably set to repeat the algorithmic process steps once again using this second initial pattern.
In accordance with the method disclosed herein, even when the optical characteristics of the design obtained by the repetition of a series of algorithmic process steps show no progress in improvement, then the algorithm may recover from this stacked condition by restarting from the second initial pattern.
Preferably, the second initial pattern may be chosen which is generated by either increasing or decreasing the refractive index or the thickness in the second selected patterns having the most appropriate optical characteristics obtained in the preceding process steps.
In accordance with the method disclosed herein, the information about optical elements, effective to the improvement of optical characteristics, in the patterns generated until the optical characteristics have been matched with, may be effectively used for the second initial pattern, allowing better and faster design of multilayered optical filters with better optical characteristics.
It is preferable to perform selection in the selecting step or the first and second selecting steps based on the order of Qj, largest-first, the Qj being given by:                     Q        =                  1                      {                                          ∑                λ                            ⁢                              xe2x80x83                            ⁢                                                (                                                            Rj                      ⁡                                              (                        λ                        )                                                              -                                          Rr                      ⁡                                              (                        λ                        )                                                                              )                                2                                      }                                              (        2        )            
where Rj(xcex) is the reflectance characteristics at each wavelength xcex obtained from the pattern combination of elements in the matrix Xi, Rr(xcex) is the desired reflectance characteristics.
If the disjunction X of the reflectance of a pattern combination from the desired reflectance characteristics, i.e., the denominator item of Q shrinks by the convergence, and the difference of X among patterns becomes small, larger difference among patterns can be taken because the Q is used as the fitness. Therefore finer extraction becomes possible even when the difference of X among patterns is small.
When the predetermined value of increasing or decreasing the refractive index and the predetermined value of increasing or decreasing the thickness in the second reproducting/mutating step is set to be 2 through 50 times, respectively, of the predetermined value of increasing or decreasing the refractive index and the predetermined value of increasing or decreasing the thickness in the first reproducting/mutating step, the convergence, around the solution may increase and the most appropriate solution may be extracted faster.
When the predetermined value of increasing or decreasing the refractive index and the predetermined value of increasing or decreasing the thickness in the second reproducting/mutating step is set to be 2 through 25 times of the predetermined value of increasing or decreasing the refractive index and the predetermined value of increasing or decreasing the thickness in the first reproducting/mutating step, the convergence around the solution increases more and the most appropriate solution may be extracted more faster.
The method of operating genetic algorithm in accordance with the present invention comprises:
pattern group generating step for generating pattern group consisted of a plurality of mutually different patterns, each of which patterns comprises elemental matrices Xi, and given by
P=(X1, X2, X3 . . . , XS)xe2x80x83xe2x80x83(1)
a manipulating step for extracting a predetermined number of patterns from the pattern group and operate on the elements of these patterns to generate operated patterns;
a selecting step for selecting the same number of patterns having mutually different characteristics from the extracted patterns and operated patterns based on the characteristics obtained from these patterns;
a substituting step for adding a predetermined patterns selected in the selecting step into the pattern group in place of the extracted patterns; and
a repeating step for repeating a series of algorithmic process steps comprised of the operating step, the selecting step, and the substituting step, until the best characteristics in the preceding pattern group obtained in the algorithmic process steps may conform to the desired error range for the desired characteristics.
In accordance with the method of operating on a genetic algorithm, in the GA, patterns having the identical elements in the selected patterns may not coexist, thus preventing the occupation of selected patterns by the pattern having the identical elements as well as the occupation of pattern groups, in order to allowing retrieval search to proceed until the best solution is found.
Preferably, the manipulating step may comprise a cross over step for extracting at least one set of a pair of patterns consisted of mutually different elements, swapping a part of the matrix in the patterns between thus extracted pattern pair to generate crossed over patterns.
In accordance with the method disclosed herein, since the cross-over is performed between patterns having mutually different elements, the crossed over patterns may be prevented from being identical to the extracted patterns. In addition, in the same process step, a new pattern having partial combination of elements effective to find the best solution in the pattern may be generated.
Preferably, the manipulating step may comprise a mutating step for extracting a predetermined number of patterns, mutating a part of the matrix of the pattern in the extracted patterns to generate mutated patterns.
In accordance with the method disclosed herein, a new pattern having partial combination of elements effective to find the best solution in the pattern and completely new elements in other parts may be generated.
Preferably, mutation method may be either a method of increasing or decreasing any element constituting the pattern by the predetermined amount of mutation, or substituting with one of predetermined candidate elements.
Former method may be effective when the genetic algorithm is applied to such a problem of finding the best solution that a solution of contiguously transforming functions should be determined, while on the other hand the latter may be effective when the genetic algorithmic is applied to such a problem of finding the best solution of combination that uses dissociative candidates.
Preferably, the operating step may comprise, in addition to the cross-over step, a mutating step for extracting a predetermined number of patterns and mutating a part of matrix of the patterns in the extracted patterns to generate mutated patterns.
The relationships between the cross-over step and the mutation step in the operating step is preferably such that the cross-over may be performed at first and then the mutation step may be performed thereafter. However, the mutation may be performed at first and then the cross-over, or either one of cross-over and mutation may be selectively performed for each repetition of the series of algorithmic process steps constituted of operating step, selecting step, and substituting step, or the cross-over and mutation may be alternatively performed for each repetition of the series of algorithmic process steps constituted of operating step, selecting step, and substituting step.
In accordance with the method as described above, diverse patterns may be newly generated by making use of both cross-over and mutation.
Preferably, the patterns selected in the selecting step may be comprised of the pattern having the best characteristics and the patterns selected by the roulette method.
In accordance with the method as described above, if there are the same patterns in the pattern groups comprised of manipulated patterns and extracted patterns, the best pattern and another pattern that is comprised of elements different from the best pattern and of elements mutually different each from other may be selected.
Preferably, the patterns selected in the selecting step may be comprised of the pattern having the best characteristics and the patterns selected by the random number method.
In accordance with the method as described above, if there are the same patterns in the pattern groups comprised of manipulated patterns and extracted patterns, a pattern may be selected which is comprised of elements different from the best pattern and of elements mutually different each from other.
Preferably, when the substitution step comprises a comparing step for comparing the characteristics of each pattern in the pattern group to be substituted in the substitution step with the characteristics of selected pattern, if there is a pattern having the identical characteristics to that of the selected pattern in the pattern group to be substituted in the substitution step, the substitution step may be omitted to proceed immediately to the operating step.
In accordance with the method disclosed herein, if there is already the selected pattern in the pattern group, the operating step may be repeated to prevent the identical patterns from occupying to allowing retrieval search to proceed until the best solution is found.
Although the steps of operating, substituting, and determining whether the algorithm has been completed, use the characteristics specific of patterns, the fitness of characteristics specific to patterns for each patterns with respect to the target characteristics may be determined and used instead. The decision of end of algorithm in this case is preferably such that the difference between the best fitness in the pattern group and the target fitness may be fitted into the error range of the target.
In accordance with the method disclosed herein, if the pattern characteristics are expressed by a plurality of values, the object to be compared with may be one fitness indication by determining the fitness with respect to the target characteristics, allowing the computational cost of comparison to be reduced.
The best values most suitable to the thickness of each layer and the refractive index may be:readily determined when designing multilayered optical filters by applying the method of operating on the genetic algorithm in accordance with the present invention. In such a case the elements of matrix Xi in the patterns should preferably be the thickness di and refractive index ni of the layer i.
In accordance with the method disclosed herein, the thickness di and refractive index ni of the layer i, the principal elements constituting the multilayered optical filters, may be simultaneously optimized, enabling larger freedom of design.
Additional objects and advantages of the invention will be according to part in the description which follows and in part will be obvious from the description, or may be learned by practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims.